A collection of problems on standing waves

Question 1

A string of length L is clamped at each end and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves cannot be:

  1. L/2
  2. L
  3. 2L/3
  4. 2L
  5. 4L

Question 2

If the speed of sound is 340 m/s, the length of the shortest open-closed pipe that resonates at 218 Hz is:

  1. 23 cm
  2. 17 cm
  3. 39 cm
  4. 78 cm
  5. 1.6 cm

Question 3

At 20^\circ {\rm C}, a pipe open at both ends resonates at a frequency of 440 Hz. At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than …

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Heat transferred along two paths

JEE Advanced 2014 Paper 1, Question 20

A thermodynamic system is taken from an initial state i with internal energy U_{i} = 100 \, {\rm J} to the final state f along two different paths i a f and i b f, as schematically shown in the figure. The work done by the system along the paths a f, i b and b f are W_{a f} = 200 \, {\rm J}, W_{i b} = 50 \, {\rm J} and W_{b f} = 100 \, {\rm J} respectively. The heat supplied to the system along the path i a f, i b and b f are Q_{i a f}, Q_{i b} and Q_{b f} respectively. If the internal energy of the system in the state b is U_{b} = 200 \, {\rm J} and Q_{i a f} = 500 \, {\rm J}, the ratio Q_{b f}/Q_{i b} is

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The problem gives us partial information about internal energies, heat transferred, and work done at various points in the PV diagram. We …

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A collection of Doppler effect problems

Here is a set of four problems on the Doppler shift of sound waves. The solutions to the problems are given at the end. If you need a refresher on the Doppler effect, the following note might be useful: How does Doppler effect work?

Question 1

While standing at a crosswalk, you hear a frequency of 560 Hz from an approaching police car. After the police car passes and is moving away from you, you hear a frequency of 480 Hz. What is the speed of the police car (take speed of sound to be v=343 m/s)?

  1. 13.1 m/s
  2. 21.1 m/s
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An adiabatic bubble

IIT-JEE 2008 Paper 1, Question 38,39,40

A small spherical monoatomic ideal gas bubble \left(\gamma=\frac{5}{3}\right) is trapped inside a liquid of density \rho_{\ell} (see figure below). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_{0}, the height of the liquid is H and the atmospheric pressure is P_{0} (Neglect surface tension).

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1. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

  1. Only the force of gravity
  2. The force due to gravity and the force due
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